The present invention relates to a system for compressing and reconstructing (decompressing) signals, including signals representing physical data such as terrain. Such signals may be computer-constructed data, empirically derived images or signals, or in general any information or data representing actual or simulated phenomena.
After compression of data representing a terrain, digital terrain elevation (or images, indeed any graph) data (“DTED”), a common problem is accurate reconstruction of terrain features, such as the slope. Given digitized data representing terrain elevation, or indeed any graph in two or more dimensions at a data point (x,y) (or the multiple dimension extension at a data point (x1, . . . , xn)), it is highly useful to be able to compress and decompress the data in such a way that terrain—or, more generally, graph or image features—are accurately reconstructed.
Conventional systems in current use compress the data, store or transmit it as needed, and at a later point reconstruct the data from the compressed-data files. This can lead to large errors in derived quantities obtained from the reconstructed data, in particular when the gradient of the reconstructed data is taken.
The gradient of the original data is often of considerable interest. In the case of DTED, it may be important for aircraft to be aware of the precise terrain slopes, and the errors introduced by determining gradients from reconstructed data may be too great to be of practical use for many applications.
Especially for lossy compression techniques, a reconstructed image generally does not have the same values for the norm of the gradient that the original image had. In fact, errors in the gradient are often quite large for higher compression ratios. These errors are quite significant since the accuracy of the terrain slope is crucial in many areas, e.g. landing of aircraft in navigation exercises.
Accordingly, a system is needed that can compress and reconstruct multidimensional data, such as terrain data or other signals, with an increased accuracy in the reconstructed information, and in particular in the gradients that are determined from the reconstructed data, and the norms of those gradients.